Topics
Electric Charges and Fields
- Electric Charge
- Conductors and Insulators
- Basic Properties of Electric Charge
- Coulomb’s Law
- Forces between Multiple Charges
- Electric Field
- Electric Field Due to a System of Charges
- Physical Significance of Electric Field
- Electric Field Lines
- Electric Flux
- Electric Dipole
- Dipole in a Uniform External Field
- Continuous Charge Distribution
- Gauss’s Law
- Application of Gauss' Law
Electrostatics
Electrostatic Potential and Capacitance
- Electric Potential and Potential Energy
- Electrostatic Potential
- Electric Potential Due to a Point Charge
- Potential Due to an Electric Dipole
- Potential due to a System of Charges
- Equipotential Surfaces
- Relation Between Electric Field and Electrostatic Potential
- Potential Energy of a System of Charges
- Potential Energy of a Single Charge
- Potential Energy of a System of Two Charges in an External Field
- Potential Energy of a Dipole in an External Field
- Electrostatics of Conductors
- Dielectrics and Polarisation
- Capacitors and Capacitance
- The Parallel Plate Capacitor
- Effect of Dielectric on Capacitance
- Combination of Capacitors
- Energy Stored in a Charged Capacitor
Current Electricity
Current Electricity
- Electric Current
- Electric Currents in Conductors
- Ohm's Law
- Drift of Electrons and the Origin of Resistivity
- Mobility of Electrons
- Limitations of Ohm’s Law
- Resistivity of Various Materials
- Temperature Dependence of Resistivity
- Electrical Energy and Power in Conductors
- Cells, EMF, and Internal Resistance
- Cells in Series and in Parallel
- Kirchhoff’s Laws
- Wheatstone Bridge
Magnetic Effects of Current and Magnetism
Moving Charges and Magnetism
- Electromagnetism
- Magnetic force
- Motion in a Magnetic Field
- Magnetic Field Due to a Current Element, Biot-savart Law
- Magnetic Field on the Axis of a Circular Current-Carrying Loop
- Ampere’s Circuital Law
- Solenoid
- Force Between Two Parallel Currents (Ampere’s Law)
- Torque on a Rectangular Current Loop in a Uniform Magnetic Field
- Circular Current Loop as a Magnetic Dipole
- Moving Coil Galvanometer
Electromagnetic Induction and Alternating Currents
Magnetism and Matter
Electromagnetic Waves
Optics
Electromagnetic Induction
Dual Nature of Radiation and Matter
Alternating Current
- AC Voltage Applied to a Resistor
- Representation of AC Current and Voltage by Rotating Vectors - Phasors
- AC Voltage Applied to an Inductor
- AC Voltage Applied to a Capacitor
- AC Voltage Applied to a Series LCR Circuit
- Phasor-diagram Solution
- Resonance
- Power in AC Circuit
- Transformers
- Overview: AC Circuits
Atoms and Nuclei
Electromagnetic Waves
- Concept of Electromagnetic Waves
- Displacement Current
- Sources of Electromagnetic Waves
- Nature of Electromagnetic Waves
- Electromagnetic Spectrum
- Overview of Electromagnetic Waves
Electronic Devices
Ray Optics and Optical Instruments
- Ray Optics Or Geometrical Optics
- Reflection of Light by Spherical Mirrors
- Sign Convention for Reflection by Spherical Mirrors
- Focal Length of Spherical Mirrors
- Mirror Equation of Spherical Mirrors
- Refraction of Light
- Total Internal Reflection
- Applications of Total Internal Reflection
- Refraction at a Spherical Surfaces
- Refraction by a Lens
- Power of a Lens
- Combined Focal Length of Two Thin Lenses in Contact
- Refraction of Light Through a Prism
- Optical Instruments
- Microscope and it’s types
- Telescope
- Overview of Ray Optics and Optical Instruments
Communication Systems
Wave Optics
- Concept of Wave Optics
- Huygens Principle
- Refraction of a Plane Wave
- Refraction at a Rarer Medium
- Reflection of a Plane Wave by a Plane Surface
- Coherent and Incoherent Addition of Waves
- Interference of Light Waves and Young’s Experiment
- Diffraction of Light
- The Single Slit
- Seeing the Single Slit Diffraction Pattern
- Polarisation of Light
- Overview: Wave Optics
The Special Theory of Relativity
Dual Nature of Radiation and Matter
- Understanding Dual Nature of Radiation and Matter
- Electron Emission
- Photoelectric Effect - Hertz’s Observations
- Photoelectric Effect - Hallwachs’ and Lenard’s Observations
- Experimental Study of Photoelectric Effect
- Effects of Intensity and Frequency on Photocurrent
- Photoelectric Effect and Wave Theory of Light
- Einstein’s Photoelectric Equation: Energy Quantum of Radiation
- Particle Nature of Light: The Photon
- Wave Nature of Matter
- Overview: Dual Nature of Radiation and Matter
Atoms
Nuclei
- Atomic Masses and Composition of Nucleus
- Size of the Nucleus
- Mass - Energy
- Nuclear Binding Energy
- Nuclear Force
- Radioactivity
- Forms of Energy > Nuclear Energy
- Nuclear Fission
- Nuclear Fusion
- Controlled Thermonuclear Fusion
- Overview: Nuclei
Semiconductor Electronics - Materials, Devices and Simple Circuits
- Concept of Semiconductor Electronics
- Classification of Metals, Conductors and Semiconductors
- Intrinsic Semiconductor
- Extrinsic Semiconductor
- n-type Semiconductor
- p-type Semiconductor
- Diode or p-n Junction
- Semiconductor Diode
- Application of Junction Diode as a Rectifier
- Overview: Semiconductor Electronics
Communication Systems
- Detection of Amplitude Modulated Wave
- Production of Amplitude Modulated Wave
- Basic Terminology Used in Electronic Communication Systems
- Sinusoidal Waves
- Modulation and Its Necessity
- Amplitude Modulation (AM)
- Need for Modulation and Demodulation
- Satellite Communication
- Propagation of EM Waves
- Bandwidth of Transmission Medium
- Bandwidth of Signals
The Special Theory of Relativity
- The Special Theory of Relativity
- The Principle of Relativity
- Maxwell'S Laws
- Kinematical Consequences
- Dynamics at Large Velocity
- Energy and Momentum
- The Ultimate Speed
- Twin Paradox
Estimated time: 7 minutes
CBSE: Class 12
Core Idea: Electrostatic Analog
The field of a bar magnet at large distances can be obtained from the field of an electric dipole by making the following replacements:
| Electrostatics | Magnetism |
|---|---|
| Electric field E | Magnetic field B |
| Electric dipole moment p | Magnetic dipole moment m |
| \[\frac {1}{4πϵ_0}\] | \[\frac {μ_0}{4π}\] |
Replacement Rule
- Replace E by B
- Replace p by m
- Replace \[\frac {1}{4πϵ_0}\] by [\frac {μ_0}{4π}\]
For a short bar magnet, the magnetic field on the equatorial line is:
Beq = −\[\frac {μ_0}{4π}\]\[\frac {m}{r^3}\]
The negative sign indicates that the direction of the field is opposite to the magnetic dipole moment vector.
For a short bar magnet, the magnetic field on the axial line is:
Bax = \[\frac {μ_0}{4π}\]\[\frac {m}{r^3}\]
This field is along the direction of the dipole moment vector.
CBSE: Class 12
The Dipole Analogy
CBSE: Class 12
Example
Step 1: Understand the setup
- There are two identical magnetic needles (dipoles): P at O (fixed) and Q placed at different positions around P.
- Each position of Q (Q₁, Q₂, …, Q₆) has its own direction of magnetic moment mQ.
Step 2: Recall field directions of P
Use the magnetic dipole field rules for P:
- On the axial line of P: BP is along mP.
- On the equatorial line of P: BP is opposite to mP.
Step 3: Use the equilibrium rule
For Q in the field of P:
- If mQ is parallel to BP → equilibrium is stable (minimum potential energy).
- If mQ is antiparallel to BP → equilibrium is unstable (maximum potential energy).
- If mQ is neither parallel nor antiparallel → not in equilibrium (net torque not zero).
Step 4: Check each configuration (using the rule)
Not in equilibrium:
- Configurations PQ1 and PQ2 (because mQ is not along or opposite to BP).
Stable equilibrium:
- Configurations PQ3 and PQ6 (here mQ is parallel to BP).
Unstable equilibrium:
- Configurations PQ5 and PQ4 (here mQ is antiparallel to BP).
Step 5: Lowest potential energy configuration
- Lowest potential energy happens when mQ is parallel to BP and the angle is zero.
- Among all shown positions, this is configuration PQ6, so PQ6 has the lowest potential energy.
